Many if not most "short form" birth certificates-- they are commonly called "birth certificate abstracts" as that's what they are-- contain all the information required. A quick google image search shows that both the NY and HI "short form" birth certificates contain all this information. I can personally vouch for Cook County and the State of Illinois-- abstracts from them have this information and always have. This 'new' rule provides no indication at all that State is no longer accepting certified birth abstracts that have all of the required information, or that they plan not to accept them in the future.
I apologize for the confusion. Where I was born, are called wallet size and full size. I will edit my post to reflect with and without the parents name, because listing each and every jurisdictions name for the form with and without such names is pretty silly.